If white light is incident on the diamond at 30 degrees, what is the angle of refraction for red and blue light?
The refractive index n of a diamond for red light of 656 nm is 2.410; for blue light of 434 nm, n is 2.410.
The refractive index of a diamond for light of different colors is not the same. That is what results in the optics displayed by diamonds. But you have given the refractive index for red as well as blue light as 2.410.
The angle of incidence is given as 30 degrees. The angle of refraction can be arrived at by using Snell's Law. According to Snell's law, if the angle of incidence is Ai, the angle of refraction is Af, the refractive index of the first medium is n1 and that of the second medium is n2, we have sin Ai/ sin Af = n2/ n1. I take the first medium is air and has a refractive index of 1.
So we get, sin 30 / sin Af = 2.410
=> sin Af = sin 30/2.410 = 0.5/ 2.410 = 0.2074
Af = arc sin 0.2074 = 11.97 degrees.
The angle of refraction for both blue as well as red light, using the information given, is 11.97 degrees.